Usable Rules for Context-Sensitive Rewrite Systems

Abstract

Recently, the dependency pairs (DP) approach has been generalized to context-sensitive rewriting (CSR). Although the context-sensitive dependency pairs (CS-DP) approachprovides a very good basis for proving termination of CSR, the current developments basically correspond to a ten-years-old DP approach. Thus, the task of adapting all recently introduced dependency pairs techniques to get a more powerful approach becomes an important issue. In this direction, usable rulesare one of the most interesting and powerful notions. Actually usable rule have been investigated in connection with proofs of innermost terminationof CSR. However, the existing results apply to a quite restricted class of systems. In this paper, we introduce a notion of usable rules that can be used in proofs of termination of CSR with arbitrary systems. Our benchmarks show that the performance of the CS-DP approach is much better when such usable rules are considered in proofs of termination of CSR.